Im sure many of us have gone through exactly wat you have, but its human nature and u gotta love it. Firstly i doubt she's the one your gonna marry and live for the rest of your life with (could happen though, dont get me wrong).
Now to the good bit *

: the thing is wen your in a friendship like you have with this girl, sometimes silence is the best option. *The ability to still feel comfortable with silence (for a short while) is one great thing to have with a friend like this. *
i think the more you try and impress her the more you might get into trouble. *wat i like to do is do interesting things, have a passion, know something in and out, have great experiences (holidays, adventures, etc). *Wat this does is create massive options for things to talk bout, wen she asks wat u did last weekend, you have all these things to talk bout and they will be unique and interesting. *imagine if your asnwer was "i went skydiving" compared to "watched tv and babysitted my sister" the latter immediately puts a dead end to the conversation. *being funny is a bonus...but dont try to hard, women and sense that. *its also great to have a few mental notes of wat u can talk bout, but wen it comes down to it, ull probably be having too much fun and talking bout many more other things u wont talk bout these, remember these are just back up topics. a very good thing to do also is not just talk bout yourself...ask her questions, draw it out of her, im sure she likes to talk bout herself and this way you get to know her better and you dont have to talk as much.
Most importantly, and ill say again most importantly it is to be yourself. *you are not spose to impress her with someone who u want to be, or are not, your supppose to impress her with who you really are. *Lying is a big no no!
i say after 1 week of seeing her, its a bit too early to just come out and say how you feel, but u could instead say it through actions, just spend more time with her or be there for her, help her out, or extend your hand of help. *Maybe the most you could say is ill b thinking bout you tonight, or after a day with her, say you had a great time, that's prolly wat i would stay too for a while.
good luck *

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*you'll do fine, trust me...if u be yourself.
Enjoy the chase, remember the butterflies!